With QToolBox, which setting to have page be only its content size?

Unfortunately you can't do that directly because it will span all the available space that the title widgets don't occupy. You can emulate what you want by setting a fixed height on the QToolBox if you know the exact height your page(s). But you do not want to do that in practise.

If you want the behavior you ask for then you need to write your own custom control. It doesn't have to be hard. Use a QVBoxLayout and fill into it items of a custom class, let's call it ToolItem, which is a QWidget with a title (perhaps a button to show/hide) and another QWidget for showing the contents that is either visible or not.

The following very simple example will toggle the visibility of the ToolItem when it is clicked. And only when visible will it occupy any space.

class ToolItem : public QWidget {
public:
  ToolItem(const QString &title, QWidget *item) : item(item) {
    QVBoxLayout *layout = new QVBoxLayout;
    layout->setContentsMargins(0, 0, 0, 0);
    layout->addWidget(new QLabel(title));
    layout->addWidget(item);    
    setLayout(layout);

    item->setVisible(false);
  }

protected:
  void mousePressEvent(QMouseEvent *event) {
    item->setVisible(!item->isVisible());
  }

private:
  QWidget *item;
};

class ToolBox : public QWidget {
public:
  ToolBox() : layout(new QVBoxLayout) {
    setLayout(layout);
  }

  void addItem(ToolItem *item) {
    // Remove last spacer item if present.
    int count = layout->count();
    if (count > 1) {
      layout->removeItem(layout->itemAt(count - 1));
    }

    // Add item and make sure it stretches the remaining space.
    layout->addWidget(item);    
    layout->addStretch();
  }

private:
  QVBoxLayout *layout;
};

And simple usage of it:

QWidget *window = new QWidget;
window->setWindowTitle("QToolBox Example");

QListWidget *list = new QListWidget;
list->addItem("One");
list->addItem("Two");
list->addItem("Three");

ToolBox *toolBox = new ToolBox;
toolBox->addItem(new ToolItem("Title 1", new QLabel("Some text here")));
toolBox->addItem(new ToolItem("Title 2", list));
toolBox->addItem(new ToolItem("Title 3", new QLabel("Lorem Ipsum..")));  

QVBoxLayout *layout = new QVBoxLayout;
layout->addWidget(toolBox);

window->setLayout(layout);
window->resize(500, 500);
window->show();

You can now tweak it to look like the QToolBox if needed.

Please don't hesitate to ask follow-up questions.

The example shown from Qt Designer may not be using a QToolBox, which behaves more like a stacked tab widget only displaying a single page at a time. The example in Qt Designer appears to be a QTreeWidget with custom drawing or styling.